FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Volatility and Distribution
In a lognormal model with dr = σ·r dw, the annualized percentage (proportional) volatility is 20%. If the short rate is 5.00%, what is the annualized basis-point volatility, and what happens when the rate rises to 8.00%?
Basis-point volatility equals percentage volatility times the rate: 20% × 5% = 100 bps. When the rate rises to 8%, it becomes 20% × 8% = 160 bps, since in a lognormal model absolute volatility scales with the rate level.
- A100 bps at 5%; rises to 160 bps at 8%Correct
- B20 bps at 5%; rises to 32 bps at 8%
- C100 bps at 5%; stays at 100 bps at 8%
- D250 bps at 5%; falls to 156 bps at 8%
Explanation
Basis-point volatility = σ·r = 0.20 × 5% = 1.00% = 100 bps. At 8%, it is 0.20 × 8% = 1.60% = 160 bps. Staying at 100 bps would be the normal-model result.
Did you get it right without looking?
One question tells you little. A timed set on The Art of Term Structure Models: Volatility and Distribution shows your real accuracy, how long you take and where you lose marks.
More The Art of Term Structure Models: Volatility and Distribution questions
- In a Ho-Lee model with constant volatility σ = 1.00% per year, a trader considers the distribution of the short rate 4 years ahead. Ignoring…
- A desk calibrates a CIR model and a Vasicek model to the same current yield curve. Compared with Vasicek, which feature of the CIR model is …
- A quant has a Ho-Lee model with constant σ = 1.20%. Over a two-period tree, the drifts are λ1 and λ2. She wants to know how the recombining …
- A risk manager compares two Vasicek calibrations with the same σ and θ: Model A has k = 0.10 and Model B has k = 0.50. Which conclusion abou…
- A risk analyst compares a normal (Ho-Lee type) short-rate model with a lognormal (Black-Karasinski type) short-rate model, both calibrated t…
- In a lognormal short-rate model dr = a·r·dt + σ·r·dw, the current short rate is 5% and annual volatility σ is 20%. What is the approximate o…